Production Mechanisms of isoscalar pseudotensor mesons in pion and kaon induced reactions

TL;DR

This work addresses the production of four predicted isoscalar pseudotensor mesons, $η_2( ext{4D})$, $η'_2( ext{2D})$, $η'_2( ext{3D})$, and $η'_2( ext{4D})$, in $ ext{π}^-$- and $ ext{K}^-$-induced reactions. It combines an effective Lagrangian framework with Regge trajectory phenomenology to model the forward, high-energy regime and to compute both total and differential cross sections for $ ext{π}^- p o η_2 n$ and $ ext{K}^- p o η_2 Λ$. The study finds a clear production selectivity: $η_2( ext{4D})$ is more readily produced in pion-induced processes, whereas the $η'_2( ext{2D,3D,4D})$ states are favored in kaon-induced reactions, each with characteristic beam-momentum peaks and forward-peaked angular distributions. These predictions, validated against known data for a related state, provide concrete guidance for future experimental searches at facilities such as J-PARC, COMPASS, and SPS@CERN, while noting uncertainties from model choices and SU(3) flavor assumptions.

Abstract

The recent observation of the X(2600) resonance by the BESIII Collaboration has motivated a renewed interest in the spectroscopy of light mesons, particularly pseudotensor states. However, a significant theoretical gap exists in the poorly explored spectrum of isoscalar pseudotensor mesons, where several predicted radial excitations remain unobserved. To address this, we investigate the production of four such states ($η_2(4D)$, $η'_2(2D)$, $η'_2(3D)$, and $η'_2(4D)$) employing an effective Lagrangian approach combined with Regge trajectory phenomenology to describe the high-energy behavior of the reactions. Our calculations reveal a distinct production selectivity: the $η_2(4D)$ state is more prominent in pion induced ($π^- p \to η_2 n$) reactions, whereas the $η'_2(2D, 3D, 4D)$ states are preferentially produced in kaon induced ($K^- p \to η_2 Λ$) processes. Moreover, the total cross sections for these states exhibit characteristic peaks at specific beam momenta, providing clear kinematic windows for their discovery. This study provides the first comprehensive theoretical predictions for the production cross sections of these predicted mesons, offering crucial guidance for future experimental searches.

Figures (6)

• Figure 1: Feynman diagrams for (a) pion induced and (b) kaon induced production of the $\eta_2$ meson. The $t$-channel exchange is dominated by the $a_2$ meson in (a) and the $K_2^*$ meson in (b).
• Figure 2: Total cross section for the $\pi^{-} p\to\pi_2^- (1670) p$ reaction. The red solid line represents the result of our Regge model calculation. The experimental data are taken from Ref. Ascoli:1973nj
• Figure 3: Total cross section for the $\pi^{-} p\to\eta_2n$ reaction in the Regge model.
• Figure 4: The differential cross section $d\sigma/d\cos\theta$ of the $\eta_2(\mathrm{4D})$ , $\eta_2^{'}(\mathrm{2D})$, $\eta_2^{'}(\mathrm{3D})$, and $\eta_2^{'}(\mathrm{4D})$ production for the $\pi^{-} p\to\eta_2n$ reaction at different $P_{\text{Lab}}$ energies.
• Figure 5: Total cross section for the $K^- p \to\eta_2 \Lambda$ reaction in the Regge model.